Question

three unbiased dice of different colours are rolled. The probability that the same number appears on atleast two of the three dice is

Answer 1

All possible outcomes:

{(1,1,1), (1,1,2), (1,1,3), (1,1,4), (1,1,5), (1,1,6),

(1,2,1), …, (1,2,6),

.

.

.

(6,6,1), … (6,6,6)} So, in total 6 X 6 X 6 possible outcomes.
events are nothing but the sum of the probabilities 1/6 in each case.

Since 6 possible numbers are there hence required probability=6*(1/6)*(1/6)*(1/6)=1/36

Answer 2

Answer:

p:event of different numbers on dices

required probability =1-p

p=6*5*4/(216)

=1-5/9=4/9

4/9